This exam will cover material from sections 5.1, and 7.1-7.3. Specifically excluded is material related to electrical circuits in section 5.1. The problems will be of a similar type to the homework and examples from lecture. At the time of the exam you will be provided with a table of Laplace Transforms, similar to that used on Quiz 8 (or see Theorem 7.1.1 on page 258 in your textbook). The table will also include the Laplace transform for the unit step function by itself or multiplied by another function, f(t-a) . There will be at least one application problem involving mass-spring systems; you may be asked to set-up the initial conditions, but not the ODE.

While most questions will require solving a given initial value problem, there will be other types. Among the possibilities:

• Find the Laplace Transform (using table if necessary).
  • For what values of s does the transform exist?
  • Rewrite a piecewise continuous function in terms of unit step functions, and find the Laplace Transform
• Find the Inverse Laplace Transform (using table if necessary).
• State the definition of the Laplace Transform, and/or use it to find the Laplace transform of a given function (may be in the form of a graph)
• Mass-Spring Systems
  • Find the equation of motion.
  • Indicate if the system is underdamped, overdamped, or critically damped.
  • Indicate if there is resonance.
  • Know what the transient and steady-state solutions are.

I will provide the paper and any additional scratch sheets you may need. Calculator rules are the same as on previous exams.